Technical Change and the Rate of Imitation
Edwin Mansfield
Econometrica, Vol. 29, No. 4. (Oct., 1961), pp. 741-766.
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Econometrica, Vol. 29, No. 4 (October 1961 )
TECHNICAL CHANGE AND THE RATE OF IMITATION*
This paper investigates the factors determining how rapidly the use of a new
technique spreads from one firm to another. A simple model is presented to
help explain differences among innovations in the rate of imitation. Deterministic and stochastic versions of this model are tested against data
showing how rapidly firms in four industries came to use twelve important
innovations. The empirical results seem quite consistent with both versions of
the model.
1.
INTRODUCTION
ONCEAN innovation is introduced by one firm, how soon do others in the
industry come to use i t ? What factors determine how rapidly they follow?
The importance of these questions has long been recognized. For example,
Mason, Clark, Dunlop, and others pointed out in 1941 the need for studies to
investigate how rapidly ". . . an innovation spreads from enterprise to
enterprise."l Eighteen years later, the need is perhaps even more obvious
than it was then.
This paper summarizes some theoretical and empirical findings regarding
the rate a t which firms follow an innovator. A simple model is presented to
help explain differences among innovations in the rate of imitation. The
model is then tested against data showing how rapidly firms in four quite
different industries came to use twelve innovations. The results-though by
no means free of difficulties-seem quite encouraging, and should help to fill a
significant gap in the literature concerning technical change.
The plan of the paper is as follows. Section 2 lists the twelve innovations
and shows how rapidly firms followed the innovator in each case. Sections 3-5
present and test a deterministic model constructed to explain the observed
differences among these rates of imitation. A stochastic version is discussed
* The work on which this report is based was supported initially by research funds
of the Graduate School of Industrial Administration and then by a contract with the
National Science Foundation. It is part of a broader study of research and technological
change that I am conducting under this contract. The paper has benefitted from discussions with a number of my colleagues a t Carnegie Institute of Technology, particularly A. Meltzer, F. Modigliani, J. Muth, and H. Wein (now a t Michigan State University). A version of it was presented a t the December, 1959 meeting of the Econometric
Society. My thanks also go to the many people in industry who provided data and
granted me interviews. Without their cooperation, the work could not have been carried
out.
1 Committee on Price Determination [7, p. 1691.
741
742
EDWIN MANSFIELD
in Section 6 . Some of the study's limitations are pointed out in Section 7 and
its conclusions are summarized in Section 8.
2.
R A T E S O F IMITATION
This section describes how rapidly the use of twelve innovations spread
from enterprise to enterprise in four industries-bituminous coal, iron and
steel, brewing, and railroads. The innovations are the shuttle car, trackless
mobile loader, and continuous mining machine (in bituminous coal) ; the byproduct coke oven, continuous wide strip mill, and continuous annealing line
for tin plate (in iron and steel) ; the pallet-loading machine, tin container, and
high-speed bottle filler (in brewing) ; and the diesel locomotive, centralized
traffic control, and car retarders (in railroads).
These innovations were chosen because of their outstanding importance
and because it seemed likely that adequate data could be obtained for them.
Excluding the tin container, all were types of heavy equipment permitting a
substantial reduction in costs. The most recent of these innovations occurred
after World War 11; the earliest was introduced before 1900. In practically
all cases, the bulk of the development work was carried out by equipment
manufacturers and patents did not impede the imitation process.2
Figure 1 shows the percentage of major firms that had introduced each
of these innovations at various points in time. To avoid misunderstanding,
note three things regarding the data in Figure 1. (1) Because of difficulties in
obtaining information concerning smaller firms and because in some cases
they could not use the innovation in any event, only firms exceeding a certain size (given in the Appendix) are included.3 (2) The percentage of firms
2 For descriptions of these innovations (and in some cases historical material), see
Association of Iron and Steel Engineers [2] for the strip mill, Camp and Francis [5] for
continuous annealing and the by-product coke oven, annual issues of Coal
on
mechanization and American Mining Congress [I] for the innovations in coal, Fortune
(January, 1936) for the tin container, American Brewer (September, 1954) for pallet
loaders and other issues for high speed fillers, Jewkes, et al. [12] for the diesel locomotive, Mansfield and Wein [17, pp. 292-31 for car retarders, and Union Switch and
Signal Co. [24] for centralized traffic control. Actually, continuous annealing was often
no cheaper than previous techniques, but it was required by customer demands.
3 For the innovations in the steel industry, we imposed the particular size limits
cited in the Appendix because, according to interviews, it seemed very unlikely that
firms smaller than this would have been able to use them. For the innovations in the
coal and brewing industries, there were no adequate published data concerning the
dates when particular firms first introduced them, and we had to get the information
directly from the firms. It seemed likely that "non-response" would be a considerable
problem among the smaller firms. This consideration, as well as the fact that the
smallest firms often could not use them, led us to impose the rather arbitrary lower
limits on size shown in the Appendix. For the railroad innovations, we took firms
RATE O F IMITATION
percent of
war nrms
Year
Percent of
Major Firm
Year
Percent of
Major Firm
1910
1920
1930
1940
1950
1960
1970 FIGURE
1.-Growth in the Percentage of Major Firms that Introduced Twelve Innovations, Bituminous Coal, Iron and Steel, Brewing, and Railroad Industries,
1890-1 958.
a. By-product coke oven (CO), diesel locomotive (DL), tin container (TC), and shuttle
car (SC).
b. Car retarder (CR), trackless mobile loader (ML), continuous mining machine (CM),
and pallet-loading machine (PL).
c. Continuous wide-strip mill (SM), centralized traffic control (CTC), continuous
annealing (CA), and highspeed bottle filler (BF).
Source: See the Appendix.
Note: For allbut the by-product coke oven and tin container, the percentages given are for every two years from the
year of initial introduction. Zerois arbitrarily set a t two years prior to the initial introduction in these charts (hut not
in the analysis). The length of the interval for the by-product coke oven is about sir years and for the tin container, it
is six months. The innovations are grouped into the three sets shown above to make i t easier to distinguish between the
various growth curves.
744
EDWIN MANSFIELD
having introduced an innovation, regardless of the scale on which they did so,
is given. The possible objections to this are largely removed by the fact that
these innovations had to be introduced on a fairly large scale. By using them
a t all, firms made a relatively heavy financial commitment.4 (3) In a given
industry, most of the firms included in the case of one innovation are also
included for the others. Thus the data for each of the innovations are quite
comparable in this regard.
Two conclusions regarding the rate of imitation emerge from Figure 1.
First, the diffusion of a new technique is generally a rather slow process.
Measuring from the date of the first successful commercial application,5 it
took 20 years or more for all the major firms to install centralized traffic control, car retarders, by-product coke ovens, and continuous annealing. Only
in the case of the pallet-loading machine, tin container, and continuous
mining machine did it take 10 years or less for all the major firms to install
them.
Second, the rate of imitation varies widely. Although it sometimes took
decades for firms to install a new technique, in other cases they followed the
innovator very quickly. For example, it took about 15 years for half of the
major pig-iron producers to use the by-product coke oven, but only about 3
years for half of the major coal producers to use the continuous mining
machine. The number of years elapsing before half the firms had introduced
an innovation varied from 0.9 to 15, the average being 7.8.
3.
A DETERMINISTIC MODEL
Why were these firms so slow to install some innovations and so quick
to install others? What factors seem to govern the rate of imitation? In this
section, we construct a simple deterministic model to explain the results in
large enough t o use car retarders and centralized traffic control and, to insure comparability, the same size limits were used for the diesel locomotive.
4 The only alternative would be to take the date when a firm first used the innovation
to produce some specified percentage of its output. I n almost every case, such data
were not published and it would have been extremely difficult, if not impossible, to
obtain them from the firms. To install a strip mill, by-product coke ovens, continuous
annealing, or car retarders, a firm had to invest many millions of dollars. Even for
shuttle cars, trackless mobile loaders, canning equipment, and pallet loaders, the
investment (although less than $100,000 usually) was by no means trivial in these
industries.
5 Note that we measure how quickly other firms followed the one that first successfully
applied the technique. Others may have tried roughly similar things before but failed.
By a successful application, we mean one where the equipment was used commercially
for years, not installed and quickly withdrawn.
745
R A T E O F IMITATION
Figure 1. In Sections 4 and 5, we test this model and see the effects of introducing some additional variables into it.
The following notation is used. Let ntj be the total number of firms on
which the results in Figure 1 for the jth innovation in the ith industry are
based6 ( j = 1,2,3; i = 1,2,3,4). Let mcr(t) be the number of these firms
having introduced this innovation at time t, ntj be the profitability of installing this innovation relative to that of alternative investments, and Su
be the investment required to install this innovation as a per cent of the
average total assets of these firms. More precise definitions of nu and Sej
are provided in Section 4. Let ilrj(t) be the proportion of "hold-outs" (firms
not using this innovation) at time t that introduce it by time t 1, i.e.,
+
Our basic hypothesis can be stated quite simply. We assume that the
proportion of "hold-outs" at time t that introduce the innovation by time
t 4-1 is a function of (1) the proportion of firms that already introduced it by
time t , (2) the profitability of installing it, (3) the size of the investment
required to install it, and (4) other unspecified variables. Allowing the function to vary among industries, we have
In the following few paragraphs, we take up the presumed effects of variation
in mcj(t)/naj,nij, and Su on Atj(t) and the reasons for interindustry differences
in the function.
First, one would expect that increases in the proportion of firms already
using an innovation would increase iltj(t).As more information and experience
accumulate, it becomes less risky to begin using it.7 Competitive pressures
That is, the total number of firms for which we have data. See Table I for the nij.
The profitability of installing each of these innovations was viewed a t first with
considerable uncertainty. For example, there was great uncertainty about maintenance
costs for diesel locomotives, "down-time" for continuous mining machines, the safety
of centralized traffic control, and the useful life of by-product coke ovens. The perceived
risks seldom disappeared after only a few firms had introduced them; in some cases
according to interviews, it took many years. This helps to account for the fact (noted
above) that the imitation process generally went on rather slowly.
This also suggests the potential importance of two variables not recognized explicitly in (2) : (1) the extent of the initial uncertainty concerning the profitability of
an innovation (depending in part on the extent of prior field testing by manufacturers),
and (2) the rate a t which this uncertainty declined. For some types of innovations, a
few installations and a relatively short period of use can cut the risks to little or nothing.
For other types, installations under many sorts of conditions and a long period of use
6
7
746
EDWIN MANSFIELD
mount and "bandwagon" effects occur. Where the profitability of using the
innovation is very difficult to estimate, the mere fact that a large proportion
of its competitors have introduced it may prompt a firm to consider it more
favorably. Both interviews with executives in the four industries and the
data in Figure 1 indicate that this is the case.8
Second, the profitability of installing the innovation would also be expected to have an important influence on Aaj(t). The more profitable this
investment is relative to others that are available, the greater is the chance
that a firm's estimate of the profitability will be high enough to compensate
for whatever risks are involved and that it will seem worthwhile to install the
new technique rather than to wait. As the difference between the profitability of this investment and that of others widens, firms tend to note and
respond to the difference more quickly. Both the interviews and the few
other studies regarding the rate of imitation suggest that this is so.9
Third, for equally profitable innovations, I i j ( t ) should tend to be smaller
for those requiring relatively large investments. One would expect this on
(to be sure of useful life, maintenance costs, etc.) are required. See Section 7 for
further discussion.
Note that all these innovations are new processes or (in the case of the tin container)
a packaging innovation. This model would not be applicable to some innovations, like
an entirely new product, where, as more firms produce it, it becomes less profitable for
others to do so. There is no evidence of significant decreases of this sort in these cases.
(E.g., as more firms introduced diesel locomotives, this did not make it less profitable for others to do so.) Moreover, the model presumes that ntf is appreciably greater
than unity (which is the case here). Finally, the data support the hypothesis in the
text (see note 8).
8 Beginning with the date when mij(t) = 1, we computed Ai5(t)and mzj(t)/nr5,
using the
intervals in the footnote to Figure 1as time units and stopping when mi5(t)= ntj. Then we
calculated the correlation between &j(t) and mtr(t)/ni5.Thecorrelation coefficients were
.77 (continuous mining machine), .85 (by-product coke oven), .49 (tin container)., 65
(centralized traffic control), .85 (continuous wide strip mill), .66 (diesel locomotive),
.52 (car retarders), .55 (bottle fillers), .96 (pallet loaders), .81 (continuous annealing),
.46 (trackless mobile loader), and .94 (shuttle car). Using a one-tailed test (which is
appropriate here), all coefficients but those for the continuous mining machine, bottle
filler, and trackless mobile loader are significant (0.05 level). All are positive.
Of course, others have stated similar hypotheses before. E.g., Schumpeter [20]
noted that "accumulating experience and vanishing obstacles" smooth the way for
imitators, and Coleman, et at. [6] noted a "snow-ball" effect. For what it is worth,
almost all the executives we interviewed considered this effect to be present. The
number of installations of the innovation or the number of firms using it might have
been used rather than the proportion of firms, but the latter seems to work quite well.
9 See Griliches [9]. Another recent study of the rate of imitation is found in Yance
[25]. Both papers focus on only one innovation (hybrid corn and the diesel locomotive).
Of course, the interfirm variation in profitability, as well as the average, could influence
Air(t).
RATE OF IMITATION
747
the grounds that firms tend to be more cautious before committing themselves
to such projects and that they often have more difficulty in financing them.
According to the interviews, this factor is often important.
Finally for equally profitable innovations requiring the same investment,
jltl(t) is likely to vary among industries. I t might be higher in one industry
than in another because firms in the former industry have less aversion to
risk, because markets are more keenly competitive, because the attitude of
the labor force toward innovation is more favorable, or because the industry
is healthier financially. Casual observation suggests that such interindustry
differences may have a significant effect on Itj(t).
Returning to equation (2), we act as if the number of firms having introduced an innovation can vary continuously rather than assume only integer
values, and we assume that &(t) can be approximated adequately within the
relevant range by a Taylor's expansion that drops third and higher order
terms. Assuming that the coefficient of (mtj(t)/ncr)2in this expansion is zero
(and the data in Figure 1 generally support this),lo we have
where additional terms contain the unspecified variables in (2). Thus,
Assuming that time is measured in fairly small units, we can use as an
approximation the corresponding differential equation"
the solution of which is
10 To test this assumption for these innovations, we used (mtr(t)/ncl)2as
an additional
independent variable in the regression described in note 8 and used the customary
analysis of variance to determine whether this resulted in a significant increase in the
explained variation. For all but continuous annealing, car retarders, and the diesel
locomotive, i t does not (and in these cases, the increase is often barely significant). Hence,
in most cases, there is no evidence that this coefficient is nonzero.
11 This is like some approximations commonly used in capital theory. E.g., one often
replaces equations like x(t I ) -x(t) = rx(t) with i ( t ) = rx(t).
+
748
EDWIN NANSFIELD
where lu is a constant of integration, Qil is the sum of all terms in (3) not
containing mu(t)/nu, and
Of course, $tr is the coefficient of mij(t)/n,in (3).
To get any further, we must impose additional constraints on the way
mii(t)can vary over time. One simple condition we can impose is that, as we
go backward in time, the number of firms having introduced the innovation
must tend to zero,l2 i.e.,
lim mij(t)= 0 .
t-t -m
Using this condition, it follows that
Thus, the growth over time in the number of firms having introduced an innovation should conform to a logistic function, an S-shaped growth curve
frequently encountered in biology and the social sciences.13
If (9) is correct, it can be shown that the rate of imitation is governed by
only one parameter-$ij.14Assuming that the sum of the unspecified terms
in ( 7 ) is uncorrelated with nil and Sij and that it can be treated as a random
error term,
1 2 Of course, other conditions could be imposed in addition or instead. For example
in Section 6, we take as given the date when a particular number of firms had installed
an innovation and we force mar(t)to equal that number a t that date. But (8) is all we
need for present purposes. Note that it implies that Qar is zero. The data described in
note 8 are consistent with this, but even if Q6,were nonzero but small (and it certainly
could not be large), (9) should be a reasonably good approximation. Note too that,
if the model holds, $6, > 0.
13 Note that things are simplified here by the fact that all firms we consider eventually introduced these innovations. (A few went out of business first, but not because
of the appearance of the innovation. See the Appendix.) Had this not been the case,
it would have been necessary either to provide a mechanism explaining the proportion
that did not do so or to take it as given. Of course, by taking only the larger firms, we
made sure that all could use these innovations. The smaller firms (that were not
potential users) are omitted. For the high-speed bottle filler, we make the reasonable
assumption that all the major firms will ultimately introduce it. Note that the argument here is different from that generally used in biology to arrive a t the logistic
function and that it explicitly.includes variables affecting its shape.
11 I t seems reasonable to take, as a measure of the rate of imitation, the time span
between (1) the date when 20 per cent (say) of the firms had introduced an innovation,
and (2) the date when 80 per cent (say) had done so. According to the model, this time
span equals 2.77 ;4 and is therefore independent of la,. If, rather than 20 and 80, we
-Pz)].
take PI and Pz,it can be shown that the time span equals 9; In [(l -P~)Pz/PI(~
749
RATE O F IMITATION
TABLE I
-
1
Parameters*
Innovation
Stf
Diesel locomotive
Centralized traffic control
Car retarders
Continuous wide strip mill
By-product coke oven
Continuous annealing
Shuttle car
Trackless mobile loader
Continuous mining machine
Tin container
High-speed bottle filler
Pallet-loading machine
I
Estimates and Root Mean Square Errorsb
Innovation
Error (Det.) Error (St.)
Diesel locomotive
Centralized traffic control
Car retarders
2.13
1.52
2.08
Continuous wide strip mill
By-product coke oven
Continuous annealing
.83
.16
.74
Shuttle car
Trackless mobile loader
Continuous mining machine
.86
.71
.81
1.34
Tin container
High-speed bottle filler
Pallet-loading machine
a
liar definitions of these parameters, see Sections 3 (nu), 4 (no and Su), and 5 (dr,, grr, t z , and Sir).
For definitions of these measures, see Sections 4
( i ~ f , $ rtj,
~ , and error (det.))
Source: See the Appeltdix and notes 6,15,16, 17,20,22,25,29,32,and 34.
and 6 (61, and error (st.)).
750
(10)
EDWIN MANSFIELD
Qeg = be
+
ae5nag
+ ae6Stg + zeg ,
where be equals at:! plus the expected value of this sum and z6.j is a random
variable with zero expected value. Hence, the expected value of $eg in a
particular industry is a linear function of nzg and Sij.
To sum up, the model leads to the following two predictions. First, the
number of firms having introduced an innovation, if plotted against time,
should approximate a logistic function. Second, the rate of imitation in a
particular industry should be higher for more profitable innovations and
innovations requiring relatively small investments. More precisely, $eg, a
measure of the rate of imitation, should be linearly related to n1.j and Sej.
4.
TESTS OF THE MODEL
We test this model in two steps: ( I ) by estimating $6,. and I t j and determining how well (9) fits the data, and (2) by seeing whether the expected
value of $u seems to be a linear function of nej and Ser. The results of these
tests suggest that the model can explain the results in Figure 1 quite well.
To carry out the first step, note that, if the model is correct, it follows
from (9) that
Measuring time in years (from 1900), treating this as a regression equation,
and using least squares (after properly weighting the observations [4]), we
derive estimates of Leg and Q 6 j (Table I ) . 1 5 TO see how well (9) can represent
the data, we insert these estimates into (9) and compare the calculated increase
over time in the number of firms having introduced each innovation with
the actual increase.
Judging merely by a visual comparison, the calculated growth curves
generally provide reasonably good approximations to the actual ones.
However, the "fit" is not uniformly good. For the railroad innovations,
there is evidence of serial correlation among the residuals, and the approximations are less satisfactory than for the other innovations. Table I contains
two rough measures of "goodness-of-fit" : the root-mean-square deviation of
15 When In [mt,(t)/nt,-mrr(t)] was infinite, the observation was omitted. The observations were one year apart for the continuous wide strip mill, continuous mining
machine, and centralized traffic control, six years apart for the by-product coke oven,
one month apart for the tin containers, and two years apart for the others. For the
high-speed bottle filler, we used all the data available thus far, but the imitation process
is not yet complete (cf. Figure 1).
R A T E O F IMITATION
751
actual from the computed number of firms having introduced the innovation16
and t.17 They
and the coefficient of correlation between In [mcj(t)/nsr-mc3(t)]
seem to bear out the general impression that (9) represents the data for most
of the innovations quite well.18
To carry out the second step, we assume that as5 and ad6 do not vary
anlong industries. 19 Thus ( 1 0) becomes
+
+
+
+
+
+
# a j = bs
a5nej
asSsj za3 ,
(12)
and, if we assume that errors in the estimates of $sf are uncorrelated with naj
and S i r , we have
(13)
J z j = bs
asnip
,
where $af is the estimate of $el derived above. Assuming that zij is distri- buted normally with constant variance, standard tests used for linear hy- potheses can be applied to determine whether a5 and a6 are nonzero. Before discussing the results of these tests, we must describe how ncj and
Szj are measured. We obtained from as many of the firms as possible estimates
of the pay-out period for the initial installation of the innovation and the
pay-out period required from investments. They were derived primarily
from correspondence, but published materials were used where possible.20
16 For each innovation, the difference between the computed and actual values of
1,. .., t y , where time is measured in the units
mij(t) was obtained for t = t:, t:
described in note 15, tz is the first date when mzj(t) = 1, and t,*;ris the first date when
mij(t) = ntj. Then the root-mean-square of these differences was obtained. Note that
this is a measure of absolute, not relative, error, and when comparing the results for
different innovations, take account of differences in nzj.
.I7 This coefficient is labeled rtj in Table I. Note that it is based on weighted observations (the weights being those suggested by Berkson [4]).
18 Of course, the logistic function is not the only one that might represent the data
fairly adequately. (E.g., the normal cumulative distribution function would probably
do as well.) And, since the actual curve has to be roughly S-shaped, it is not surprising
that it fits reasonably well. There seemed to be little point in attempting any formal
"goodness-of-fit" tests here. The number of firms considered in each case is quite
small, and the tests would not be very powerful. All that we conclude from Table I
is that (9) provides a reasonably adequate description of the data and hence that q5tj
is generally reliable as a measure of the rate of imitation.
1 9 Because of the small number of observations, we are forced to make this assumption. If data were available for more innovations, it would not be necessary. Of course,
if interindustry differences in these coefficients are statistically independent of ntj and
Sir, a 5 and a 6 can be regarded as averages and there is no real trouble.
20 A letter was sent to each firm asking ( I ) how long it took for the initial investment
in the innovation to pay for itself, and (2) what the required pay-out period was during
the relevant period. (For a definition of the pay-out period, see Swalm [22]. Both the
realized and required pay-out periods are before taxes.) Replies were received from 50
per cent of the rail roads and coal producers and 20 per cent of the steel companies and
breweries. The estimates for the railroad innovations are probably most accurate since
the firms referred us to fairly reliable published studies (see the Appendix). The data
+
752
EDWIN MANSFIELD
Then the average pay-out period required by the firms (during the relevant
period) to justify investments divided by the average pay-out period for
the innovation was used as a measure of ntj.21 To measure Su, we used the
average initial investment in the innovation as a percentage of the average
total assets of the firms (during the relevant period).22 Table I contains the
results.
Using these rather crude data, we obtained least squares estimates of the
parameters in (1 3) and tested whether they were zero. The resulting equation is
for the coal innovations are probably quite good too. The estimates for the steel innovations and the tin container are probably less accurate because they occurred so
long ago and because fewer firms provided data. Despite the fact that the averages are
probably more accurate than the individual figures and that the results werechecked with
other sources in interviews (see the Appendix), the estimates of the nrj are fairly rough.
2 1 For relatively long-lived investments, the reciprocal of the pay-out period is a
fairly adequate approximation to the rate of return. See Gordon [a] and Swalm [22].
Hence this measure of nfj is approximately equal to the average rate of return derived
(ex post) from the innovation divided by the average rate of return firms required (ex
ante) to justify investments. Of course, it would be more appropriate for firms to recognize that introducing it next year, the year after, etc., are the alternatives to introducing it now and to make an analysis like Terborgh's [23]. But as he points out, most
firms seem to make these decisions on the basis of the "rate of return" or "pay-out
period" ; and thus it seems reasonable to use such measures in a study (like this) where
we try to explain behavior, not prescribe it.
Even so, this measure is only an approximation. (1) The rate of return from the investment in an innovation is measured ex post, not ex ante. (2) The average rate
of return that could have been realized by the "hold-outs" a t a particular point in
time probably differed from the average rate of return actually realized by all firms.
Our estimates are based implicitly on the factor prices and age of old equipment (where
replacement occurred) that prevailed when the innovation was installed, and these
(and other) factors, as well as the innovation itself, do not remain unchanged. According
to the interviews, the average return that could have been realized probably varied
over time about an average that was highly correlated with our estimate, and hence
the latter provides a fair indication of the level. But the parameters describing the temporal variation about this level are among the "other" variables in (2). See Section 7
and note 40.
2 2 For the steel, coal, and brewing industries, we obtained the total assets of as
many of these firms as possible (during the relevant period) from Moody's. For the
railroads, the 1936 reproduction costs in Klein [13] were used for the firms. Estimates
of the approximate investment required to install each innovation were obtained
primarily from the interviews (described in the Appendix), and each was divided by
the average total assets of the relevant firms. Since the investment could vary considerably, the results are only approximate.
RATE O F IMITATION
753
where the top figure in the brackets pertains to the brewing industry, the
next to coal, the following to steel, and the bottom figure pertains to the
railroads. The coefficients of ntj and St5have the expected signs (indicating
that increases in ntj and decreases in Str increase the rate of imitation), and
both differ significantly from zero. As expected, there are significant interindustry difference~,the rate of imitation (for given ntj and St,) being
particularly high in brewing. These differences seem to be broadly consistent
with the hypothesis often advanced that the rate of imitation is higher in
more competitive industries, but there are too few data to warrant any real
conclusion on this score.23
Actual
Value
FIGURE
2.-Plot
of Actual
&, Against That Computed from Equation (14)' Twelve
Innovations.
Source: Table I and equation (14).
Note: The difference between an actual and computed value of
and the 45' line.
A
$rj
is equal to the vertical difference between the point
23 For a more extended statement of this hypothesis, see Robinson [19]. We encounter here the usual difficulty in measuring the "extent of competition." But most
economists would undoubtedly agree that brewing and coal are more competitive than
steel and railroads (and the average value of bs is larger in the former industries). When
six of my colleagues were asked to rank them by "competitiveness," they put brewing
first, coal second, iron and steel third, and railroads fourth. If these ranks are correlated with the estimates of bg in (14), the rank correlation coefficient is positive (.80),
but not statistically significant. (The .05 probability level is used throughout this
paper.) There are too few 'industries t o allow a reasonably powerful test of this hypothesis even if our procedures were refined somewhat, but for most rankings that seem
sensible, the data are consistent with the hypothesis (the correlation is positive).
754
E D W I N MANSFIELD
The scatter diagram in Figure 2 shows that (14) represents the data
surprisingly well. When corrected for the relatively few degrees of freedom,
the correlation coefficient is .997. Of course, one point (the tin container)
strongly affects the results. But if that point is omitted, the interindustry
differences remain much the same, the coefficients of ntj and SU keep the
same signs (the latter becoming non-significant), and the correlation coefficient, corrected for degrees of freedom, is still .97.24
Hence, the model seems to fit the data quite well. In general, the growth
in the number of users of an innovation can be approximated by a logistic
curve. And there is definite evidence that more profitable innovations and
ones requiring smaller investments had higher rates of imitation, the particular relationship being strikingly similar to the one we predicted. Though
it is no more than a simple first approximation, the model can represent the
empirical results in Figure 1 surprisingly well.
5. ADDITIONAL
FACTORS
Of course, other factors may also have been important, and their inclusion in the model may permit a significantly better explanation of the
differences among rates of imitation. Moreover, it may show that the apparent effect of the previously mentioned variables on the rate of imitation
is partly due to their influence. We turn now to a discussion of the influence
of four other factors on ;iaj(t).
First, one might expect Au(t) to be smaller if the innovation replaces
equipment that is very durable. I n such cases, there is a good chance that
a firm's old equipment still has a relatively long useful life, according to past
estimates. Although rational economic calculation might indicate that
replacement would be profitable, firms may be reluctant to scrap equipment
that is not fully written off and that will continue to serve for many years.
24 Five points should be noted. (1) The tin container is a somewhat different type
of innovation from the others and the profitability data for it are probably least
reliable (see note 20). Thus, besides its being an extreme point in Figure 2, there are
other possible grounds for excluding it, and it is reassuring to note that its exclusion
has so little effect on the results. (2) Because of the way it is constructed, the model
can only be expected to work if nlj and Su remain within certain bounds. If ntj is
close to one or Si5 is very large or both, it is likely to perform poorly. (3) One-tailed
tests are used to determine the significance of the coefficients of nlj and St5. (4) I t is
noteworthy that $it, not a very obvious measure of the rate of imitation, should be
linearly related to ncj and St5, as the model predicts. Using the result in note 14, the
number of years elapsing between when 20 per cent and when 80 per cent introduced
the innovation can easily be used instead as the dependent variable in (14). The
resulting relationship is nonlinear. (5) This model may also help to explain the empirical results Griliches [9] obtained in his excellent study of the regional acceptance of
hybrid corn, but for which he provided no formal theoretical underpinning.
RATE O F IMITATION
755
If so, &-the number of years that typically elapsed before the old equipment was replaced (before the innovation appeared)-may be one of the
excluded variables in (2), and hence $ts may be a linear function of ngj, Szj,
and dzj.25 If dtl is included in (14), we find that
(-.28)
Though there is some apparent tendency for the rate of imitation to be lower
in cases where very durable equipment had to be replaced, it is not statistically significant. (For the values of drf and the other factors discussed below,
see Table I.)
Second, one might expect &(t) to be higher if firms are expanding at a
rapid rate. If they are convinced of its superiority, the innovation will be
introduced in the new plants built to accommodate the growth in the market.
If there is little or no expansion, its introduction must often wait until the
firms decide to replace existing equipment. If gzr-the annual rate of growth
of industry sales during the period-is included in (14),
Thus, there is some apparent tendency for the rate of imitation to be higher
where output was expanding at a very rapid rate, but it is not statistically
significant.26
If we carry dl5 from (2) on and make the same assumptions we did with regard to
and S*,, it follows that 5b15should be a linear function of nu,Stj, and da,. This, of
course, is also true for the other variables discussed in this section. Estimates of dij
were obtained primarily from the interviews. If an innovation was largely a supplement
or addition to old plant (like centralized traffic control and car retarders), if it served
a different purpose than the old equipment (like canning equipment vs. bottling
equipment), and if it displaced only labor (like pallet loaders), we let
equal zero. In
such cases, there appeared to be no equipment whose durability could influence the
decision significantly. Note that the age distribution and number of units of old
equipment are also important in determining how long it takes before the first one
"wears out." I t would also have been preferable to have included the profitability of
replacing old equipment of various ages rather than just the average figure used. But
the available data would not permit this. For further discussion, see Mansfield [15].
26 Of course, the effect of gaj may depend on whether old equipment must be replaced,
how durable it is, the difference between the profitability of replacement and of installing the innovation in new plant, the extent of excess capacity a t the beginning of
the period, the size of a plant relative to the size of the market, etc. (For some relevant
25
nij
756
EDWIN M A N S ~ I E L D
Third, ilzj(t) may have increased over time. This hypothesis has been
advanced by economists on numerous occasions.27 Presumably, the reasons
for such a trend would be the evolution of better communication channels,
more sophisticated techniques to evaluate machine replacement, and more
favorable attitudes toward technological change. If tij-the year (less 190P;
when the innovation was first introducedzg-is included in (1 4 ) ,
There is some apparent tendency for the rate of imitation to increase over
time, but it is not statistically significant.
Finally, one might suppose that Azj(t) would be influenced by the phase
of the business cycle during which the innovation was first introduced.
Let 6(i equal one if the innovation is introduced in the expansion phase and
zero if it is introduced in the contraction phase.29 Including 6ij in (14),we
have
(18)
I'"'[
J f j =
-.48
-.57
+ .530ntj - .033Sii - .022 ati
(.017)
(.020)
(Y
=
.997) ,
(.045)
and the effect of au turns out to be non-significant.
Thus, our results regarding these additional factors are largely inconclusive.
Though each might be expected to have some effect, their inclusion in the
analysis does not lead to a significantly better explanation of the observed
differences in &. Their apparent effects are in the expected direction, but
da.ta for more innovations will be required before one can be reasonably sure
of the persistence and magnitude of their influence. There is no evidence
discussion, see Scitovsky [21].) The effect of this factor, like dc5,reflects the possible
unwillingness of firms to scrap existing equipment. I t would have been preferable to
have used figures on the profitability of using the innovation in new plant as well to
replace equipment of various ages, but data were not available. Note too that get may
be affected by the appearance of the innovation. For a description of the data ongat,
see the Appendix. If Scj is omitted from (15)-(IS), the coefficients of di5, get, etc.
remain non-significant.
27 E.g., Mack [14, p. 2951 and Jerome [ l l , p. XXV].
28 I.e., ti5 = t t - 1900. See note 32.
29 We used the National Bureau's reference dates (given in Moore [I 8]), to determine
whether 5
:t was a year of contraction or recovery. The residuals in Figure 2 do not seem
to be affected by whether or not an innovation was being accepted sometime during
the depression of the nineteen-thirties.
757
R A T E O F IMITATION
that the effects of the previously considered variables on the rate of imitation
are due to the operation of these factors. When these other factors are included, the coefficients of ntj and Sij and the interindustry differences
remain relatively unchanged (though the coefficient of Srj becomes nonsignificant.)
In this section, we present and test a somewhat more sophisticated, stochastic version of the model. For the jth innovation in the ith industry, let
Pti(t,k) be the probability that any one of the "hold-outs" at time t will
introduce it by time t k, and assume (for small k) that
+
where the coefficients in (20) are analogous to those in (12). To see how
closely this resembles the deterministic model, note that the ex$ected increase
in the number of users between time t and time t 1,
+
is almost identical with the expression given before for the a c t ~ aincrease
l
in
the number of users (see (4) and (5)).The only (apparent) difference is that
the terms corresponding to Qu are assumed to be zero from the start here,
whereas in Section 3 this followed from (8).30
Whereas our task in the deterministic model was to determine how the
actual number of users grows over time, our problem here is to see how the
expected number grows. To do so, we first obtain an expression for P;j(t)
-the probability that a t time t there are exactly r firms in the ith industry
that have not yet introduced the jth innovation. From (19),
where o(r2) represents terms that, if divided by k, tend to zero ask vanishes.31
To simplify things, we also assume from the beginning that the coefficients of
and St, do not vary among industries (Cf. (20)). I n the deterministic model we introduced this assumption later in the analysis.
31 To derive this expression, note that P i j ( t + k ) ) =
PTj(t) D;,-' ( t ) ,where D;,-' ( t )
is the probability that (x-v) firms begin using the innovation between time t and
time t k , given that (ntj-x) firms are using i t a t time t. From (19),
30
nzj
x:zr
+
758
EDWIN MANSFIELD
And if we subtract p:j(t) from both sides, divide by k, and let k tend to zero,
the following differential-difference equation results :
*
with the initial conditions that p;(tu) equals unity for r = ntj- 1 and zero
otherwise, and where ~ ' ; l (is
t )the time derivative of ~ ; ( t and
) te is the date
(taken as given)32 when the innovation was first introduced. From (21), it
*
follows [3] that Mt3(tt5 V)-the expected number of firms using the inno*
vation at time tz5 V-equals
+
+
where r runs up to (ntj- 1 ) / 2for ntj odd and up to ntj/2for ntj even.33
Thus, the stochastic version of the model leads to the following two
propositions. First, the expected number of firms having introduced an
*
innovation at any date subsequent to taj should be given by (22). Second,
Bu-the parameter that, for given ntj, determines the expected rate of imita-
Note two things, (1) The assumption that the probability in (19) is the same for all
"hold-outs" is obviously only a convenient simplification. Without it, the analysis
becomes extremely difficult. (2) We assume that the decisions of the "hold-outs"
between time t and time t k are independent. Hence, theprobability that one "holdo(k),
out" will introduce it between time t and time t k is [nzj-mzj(t)]%zjmtj(tjk/n.sf
and the probability that none will introduce it is I-[nzr-mtr(t)]Otrmij(t)k/nir o(k).
3 2 For all but the tin container, we use December 31 of the year during which the
innovation was first introduced by one of these firms (or if we know the month when
it was first introduced, we use that December 31 which was closest in time to it). For
the tin container, we use February 1, 1935. See Table I for the year in which each t:
falls.
33 When ncj is even, some adjustment has to be made to this expression. See Bailey
[3] for the adjustment and for a much more extensive discussion of the argument.
+
+
+
+
RATE O F IMITATION
759
tion-should be a linear function of ntj and Stj, the intercept of the function
differing among industries.
To see how well the first proposition seems to hold, we estimate elj, insert
it, nrj, and t: into (22), and compare the growth over time in the computed
number of users with the actual growth curve. Table I contains a rough
measure of "goodness-of-fit" : the root-mean-square deviation of the actual
from the computed number of users.34 Although the agreement between the
actual and computed growth curves is sometimes quite good, Table I shows
that (22) is never so accurate as (9) in representing the data. Perhaps this
is due in part to differences in the way parameters are estimated as well as
differences in the model.35
To test the second proposition, we assume that errors in the estimates of
O t j are uncorrelated with ntj and Stfand hence that
where $6, is our estimate of Orj andxi;' is arandom error term. Then, proceeding
as we did in Sections 4 and 5, we get much the same sort of results as those
obtained there. (1) We estimate the parameters in (23), find that these
estimates are almost identical with those given in (14) for the analogous
parameters,36 and conclude that the resulting equation represents the data
very well (r = .997). (2) We introduce the additional variables discussed in
Section 5 into (23) and find that their coefficients have the expected signs,
but that (except for the coefficient of ti3) all are non-significant.
Thus, the model, in either its deterministic or stochastic form, seems to
represent the empirical results in Figure 1 quite well. Although (22) does not
fit the data as well as (9) in the deterministic version, the purpose and
interpretation of these equations are quite different and hence this may not
be very surprising.37 With regard to the explanation of differences in the
34 TO estimate Oer, we used the statistic suggested by Bailey [3, p. 411 to estimate
Otr/ncland multiplied the result by nil. This estimate of Bu is biased, but we can show
that the bias is approximately equal to Otr/(ntr- I ) , which is usually quite small. These
estimates, together with the tables in Mansfield and Hensley [16], were used to calculate the growth over time in the expected number of users. The root-mean-square
errors are computed in the way described in note 16.
35 TWOparameters (Itr and q5tj) are fitted to the data in the deterministic model
whereas only ( O r j ) is fitted here. However, this is only part of the explanation (see
note 37). Note too that the differences between the computed and actual curves are
by no means random for a number of these innovations. The computed curves sometimes lie below the actual ones.
36 The only appreciable difference is that the coefficient of nil is .580 rather than
.530. 37 In the deterministic model, we fit (9) to the data in such a way as to minimize
differences between the actual and computed curves. In this model, we use the data to
estimate the curve of averages that would result if the process were repeated indefinite-
760
EDWIN MANSFIELD
rate of imitation, (23), like (13) in the deterministic model, provides an
excellent fit. The stochastic version of the model seems somewhat more
reasonable to me, but it is difficult to tell at this point whether it is a significant improvement over the simpler, deterministic version.
Before concluding, one final point should be noted regarding the dispersion
about the expected value in (22). This dispersion is often relatively large and
hence a prediction of the rate of imitation based on (22) would be fairly crude,
even if the model were correct and B i j were known in advance. To illustrate
*
this, consider an innovation where nir = 12, ti$ = 1924, and Oil = .42.
Table I1 shows the expected number of firms having introduced it at various
points in time and the relatively large standard deviation of the distribution
about this expectation. Of course, despite this variation, the model could set
useful upper and lower bounds on how long the entire process would take.38
TABLE I1
EXPECTED
VALUEAND STANDARD
DEVIATION
OF THE NUMBER
OF FIRMSHAVING
INTRODUCED
AN INNOVATION,
ASSUMING
THAT nrj = 12, tt: = 1924, AND Ocr = .42.
1924-39
Date
(Dee.31)
I
Expected
Number
1
Standard
Deviation
I
Source: Tables in Mansfield and Hensley [16]. Small errors due to interpolation are present in both theexpected
values and standard deviations.
ly. Whereas the point in the former case was to minimize differences between the
computed and actual curves, this was not the point here and hence it is not surprising
that the deterministic model seems superior in this respect.
38 For further discussion of the distribution about these expected values, see
Mansfield and Hensley [I 61 and the literature cited there.
761
RATE OF IMITATION
7.
LIMITATIONS
In evaluating these results, the limitations of the data, methods, and
scope of the investigation must be taken into account. For example, although
its scope far exceeds that of the few studies previously conducted, it nonetheless is limited to only four industries and to only a few innovations in each
one. Before concluding, it seems worthwhile to point out some of these
limitations in more detail.
First, there is the matter of scope. Although the four industries included
here vary with respect to market structure, size of firm, type of customer,
etc., they can hardly be viewed as a cross-section of American industry. For
example, none is a relatively young industry with a rapidly changing technology. In addition, the innovations included here are all important, they
generally required fairly large investments, and the imitation process was
not impeded by patents. To check and extend these results, similar studies
should be carried out for other industries and other types of innovations.
Moreover, international comparisons might be attempted.
Second, the data are not always as precise as one would like. For example,
much of the data regarding the profitability of installing an innovation had
to be obtained from questionnaires and interviews with firms. Although these
estimates were checked against others obtained from suppliers of the equipment, trade journals, etc., they are probably fairly rough. Similarly, the
estimates of the pay-out period required for investments and the durability
of old equipment are only rough. Because of these errors of measurement, the
regression coefficients in (14)-(18) are probably biased somewhat toward
zero.39
Third, the data measure the rate of imitation among large firms only. As
noted above, firms not exceeding a certain size (specified in the Appendix)
were excluded. Moreover, the rate at which firms imitated an innovator, not
the rate at which a new technique displaced an old one or the rate at which
investment in a new technique mounted, is considered here. Although these
are related topics also being studied, they were not taken up in this paper.
Fourth, various factors other than those considered here undoubtedly
exerted some influence on the rate of imitation. Variation over time in the
profitability of introducing an innovation (due to improvements, the business
39 I t can easily be shown that measurement errors, if random, have this effect.
Another limitation of the analysis is that the model can only be expected to hold for
1 and
relatively profitable innovations. Certainly, it will not hold in cases where nlj
it may do poorly if nzj is not appreciable greater than unity. But this limitation is not
very serious because if nil does not exceed unity, the innovation almost certainly will
not become generally accepted, and if nil is not much greater than unity, the innovation is probably not very important.
<
762
EDWIN MANSFIELD
cycle, etc.) is one potentially important factor that is omitted.40 Others are
the sales and promotional efforts made by the producers of the new equipment and the extent of the risks firms believed they assumed at first by
introducing an innovation.41 I could find no satisfactory way to measure
them, but perhaps further research will obviate this difficulty and disclose
the effects of these and other such factors on the rate of imitation. I suspect
that the results underestimate their influence and that data for more
innovations would show that the unexplained variation (due to their effects)
is greater than is indicated in Figure 2.
In their discussions of technological change, economists have often cited
the need for more research regarding the rate of imitation. Because an
innovation will not have its full economic impact until the imitation process
is well under way, the rate of imitation is of considerable importance. I t is
unfortunate that so little attention has been devoted to it and that consequently we know so little about the mechanism governing how rapidly
firms come to use a new technique.
My purpose in this paper has been to present and test a simple model
designed to help explain differences among process innovations in the rate of
imitation. This model is built largely around one hypothesis-that the
probability that a firm will introduce a new technique is an increasing func40 One cannot tell with any accuracy how, and to what extent, the profitability
varied in each of these cases. But, to illustrate the factors a t work, note a few broad
changes that occurred in the case of three of the innovations. (1) The appearance of
improved diesel locomotives in the Thirties and Forties increased the profitability of
introducing them and hastened their acceptance. In addition, first costs declined, the
relative prices of coal and oil changed, and the composition of the "hold-outs" varied.
(2) The demand for toluene during World War I undoubtedly accelerated the imitation
process in the case of the by-product coke oven. (3) The Depression reduced the
profitability of introducing centralized traffic control, whereas the wartime traffic
boom increased its profitability. For further discussion, see note 21. Of course, the
relative profitability may have varied less than the absolute profitability.
41 In each of these cases, there was considerable promotional effort by the producers
of the new equipment and considerable help given to the firms that used it. E.g., SemetSolvay and Koppers helped to finance by-product coke plants and provided personnel,
General Motors helped to train diesel operators, kept maintenance men a t hand, etc.
For some discussion of the perceived risks, see note 7.
Another factor that could be very important for some innovations is the presence
of patents. Still another is the development of a marked improvement in the innovation.
E.g., an innovation may be applicable a t first to only a few firms and a significant improvement is required before others use it. In a case like this, the model is clearly not
applicable. See Mansfield [15]. In each of these cases, improvements occurred, but they
were of a more gradual and less significant nature.
RATE OF IMITATION
763
tion of the proportion of firms already using it and the profitability of doing
so, but a decreasing function of the size of the investment required.42 When
confronted with data for twelve innovations, this model seems to stand up
surprisingly well. As expected, the rate of imitation tended to be faster for
innovations that were more profitable and that required relatively small
investments. An equation of the form predicted by the model can explain
practically all of the variation among the rates of imitation.
As expected, there were also interindustry differences in the rate of
imitation. WTehave too few industries really to test the hypothesis often
advanced that the rate of imitation is faster in more competitive industries,
but the differences seem to be generally in that direction. When several other
factors are included in the model, the empirical results are largely inconclusive. There was some apparent tendency for the rate of imitation to be higher
when the innovation did not replace very durable equipment, when the
firms' output was growing rapidly, and when the innovation was introduced
in the more recent past. But it was almost always statistically non-significant.
In view of the relatively small number of innovations and the uneven
quality of the data, these results are quite tentative. But even so, they should
be useful to economists concerned with the dynamics of firm behavior and
the process of economic growth. To understand how economic growth is
generated, we must know more about the way innovations occur and how
they become generally accepted. Further attempts should be made to check
and extend the results and to pursue other approaches to the particular area
considered here. We need to know much more about this and other aspects
of technological change.
Carnegie Institztte of Technology a d Yale University
APPENDIX
Iron and steel industry: For the continuous wide strip mill, all firms having more than
140,000 tons of sheet capacity in 1926 were included; for the by-product coke oven,
all firms with over 200,000 tons of pig iron capacity in 1901 were included; and for
continuous annealing of tin plate, the nine major producers of tin plate in 1935 were
included. In the case of the strip mill and coke oven, a few of these firms merged or
went out of business before installing them, and there was no choice but to exclude
them.
The date when each firm first installed a continuous wide strip mill was taken from
the Association of Iron and Steel Engineers [2]. Similar data for the coke oven were
obtained from various editions of the Directory of Iron and Steel Works of the American
4 2 This is the stochastic version of the model. In the deterministic version, we use
the proportion of "hold-outs" that introduce i t rather than this probability.
Iron and Steel Institute and issues of the Iron Trade Review and Iron Age. The date
when each firm installed continuous annealing lines was obtained from correspondence
with the firms.
The size of the investment required and the durability of replaced equipment came
from interviews. (The estimates of the pay-out periods were also checked there. Cf.
note 20.) The interviews (each about 2 hours long) were with major officials of three
steel firms, the president and research manager of a firm that builds strip mills and
continuous annealing lines, officials of a firm that builds coke ovens, and representatives of a relevant engineering association and of a trade journal. The data on growth
of output were annual industry growth rates and were for sheets during 1925-37
(strip mill), pig iron during 1900-25 (coke oven), and tin plate during 1939-56 (continuous annealing). They were taken from the Bituminous Coal A n n u a l of the Bituminous Coal Institute, Association of Iron and Steel Engineers [2], and A n n u a l Statistical
Reports of the American Iron and Steel Institute.
Railroad industry: For centralized traffic control, all Class I line-haul roads
with over 5 billion freight ton-miles in 1925 were included. For the diesel locomotives
and car retarders, essentially the same firms were included. (The Norfolk and UTestern,
a rather special case, was replaced by the New Haven and Lehigh Valley in the case
of the diesel locomotive. Some important switching roads were substituted in the
case of car retarders, an innovation in switching techniques.) An entire system is
treated here as one firm.
The date when a firm first installed centralized traffic control was usually derived
from a questionnaire filled out by the firm. For those that did not reply, estimates by
K. Healy [lo] were used. The date when each firm first installed diesel locomotives was
determined from various editions of the Interstate Commerce Commission's Statistics
of Railways. The date when each firm first installed car retarders was taken from
various issues of Railway Age.
For centralized traffic control and car retarders, some of the pay-out periods were
estimates published in the Signal Section, Proceedings of Association of American
Railroads, and the rest were obtained from questionnaires filled out by the firms. All
estimates of the pay-out period for the diesel locomotive and the pay-out period
required for investment were obtained from questionnaires. Information regarding
the size of the investment required and the durability of old equipment was obtained primarily from interviews with eight officials of six railroads (ranging from
president t o chief engineer) and three officials of a signal manufacturing firm and a
locomotive manufacturing firm. The data on growth of output were annual growth
rates for total freight ton-miles during 1925-41 (diesel locomotive) and 1925-54
(centralized traffic control and car retarders.) They were taken from the Statistics of
Railways.
Bituminous coal industry: Practically all firms producing over 4 million tons of coal
in 1956 (according t o McGraw-Hill's Keystone Coal Buyers M a n u a l ) were included. A
few firms that did strip mining predominantly were excluded in the case of the continuous mining machine, and a few had to be excluded in the case of the shuttle car
and trackless mobile loader because they would not provide the necessary data. The
date when each firm first introduced these types of equipment was usually obtained
from questionnaires filled out by the firms, but in the case of the continuous mining
machine, data for two firms that did not reply were derived from the Keystone Coal
Buyers Manual.
RATE OF IMITATION
765
Data regarding the size of the investment required and the durability of old equipment were obtained from interviews with two vice-presidents of coal firms, several
executives of firms manufacturing the equipment, employees of the Bureau of Mines,
and representatives of an independent coal research organization. The data on growth
of output were annual growth rates for bituminous coal production during 1934-51
(trackless mobile loader), 1937-51 (shuttle car), and 1947-56 (continuous mining
machine). They were taken primarily from the Bituminous Coal Annual.
Brewing industry: We tried to include all breweries with more than $1 million in
assets in 1934 (according to the Thomas Register), but several would not provide the necessary data and they could not be obtained elsewhere. The date when a firm first installed
each type of equipment was usually taken from a questionnaire that i t filled out, but
in a few cases i t was provided by manufacturers of the equipment or articles in the Brewers' ,journal. The size of the necessary investment and the durability of equipment
that was replaced were determined from interviews with a number of officials in two
breweries and sales executives of two can companies. The data on growth of output
were annual growth rates for beer production during 1935-37 (tin containers) and 195058 (pallet loading machine and high-speed bottle filler). They were taken from the
Brewers' Almanac and Business Week (June 20, 1959). The 1950-58 figures refer only
to half of these larger firms.
REFERENCES
[I] AMERICAN
MININGCONGRESS
: Coal Mine Modernization Yearbook (annual).
[2] ASSOCIATION
OF IRONAND STEELENGINEERS
: The Modern Stri? Mill (Pittsburgh,
1941).
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Technical Change and the Rate of Imitation
Edwin Mansfield
Econometrica, Vol. 29, No. 4. (Oct., 1961), pp. 741-766.
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[Footnotes]
2
A Model for the Location of a Railroad Classification Yard
Edwin Mansfield; Harold H. Wein
Management Science, Vol. 4, No. 3. (Apr., 1958), pp. 292-313.
Stable URL:
http://links.jstor.org/sici?sici=0025-1909%28195804%294%3A3%3C292%3AAMFTLO%3E2.0.CO%3B2-O
8
The Diffusion of an Innovation Among Physicians
James Coleman; Elihu Katz; Herbert Menzel
Sociometry, Vol. 20, No. 4. (Dec., 1957), pp. 253-270.
Stable URL:
http://links.jstor.org/sici?sici=0038-0431%28195712%2920%3A4%3C253%3ATDOAIA%3E2.0.CO%3B2-N
9
Hybrid Corn: An Exploration in the Economics of Technological Change
Zvi Griliches
Econometrica, Vol. 25, No. 4. (Oct., 1957), pp. 501-522.
Stable URL:
http://links.jstor.org/sici?sici=0012-9682%28195710%2925%3A4%3C501%3AHCAEIT%3E2.0.CO%3B2-A
21
The Payoff Period and the Rate of Profit
Myron J. Gordon
The Journal of Business, Vol. 28, No. 4, Capital Budgeting. (Oct., 1955), pp. 253-260.
Stable URL:
http://links.jstor.org/sici?sici=0021-9398%28195510%2928%3A4%3C253%3ATPPATR%3E2.0.CO%3B2-A
NOTE: The reference numbering from the original has been maintained in this citation list.
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24
Hybrid Corn: An Exploration in the Economics of Technological Change
Zvi Griliches
Econometrica, Vol. 25, No. 4. (Oct., 1957), pp. 501-522.
Stable URL:
http://links.jstor.org/sici?sici=0012-9682%28195710%2925%3A4%3C501%3AHCAEIT%3E2.0.CO%3B2-A
26
Economies of Scale, Competition, and European Integration
Tibor Scitovsky
The American Economic Review, Vol. 46, No. 1. (Mar., 1956), pp. 71-91.
Stable URL:
http://links.jstor.org/sici?sici=0002-8282%28195603%2946%3A1%3C71%3AEOSCAE%3E2.0.CO%3B2-8
29
Measuring Recessions
Geoffrey H. Moore
Journal of the American Statistical Association, Vol. 53, No. 282. (Jun., 1958), pp. 259-316.
Stable URL:
http://links.jstor.org/sici?sici=0162-1459%28195806%2953%3A282%3C259%3AMR%3E2.0.CO%3B2-T
References
6
The Diffusion of an Innovation Among Physicians
James Coleman; Elihu Katz; Herbert Menzel
Sociometry, Vol. 20, No. 4. (Dec., 1957), pp. 253-270.
Stable URL:
http://links.jstor.org/sici?sici=0038-0431%28195712%2920%3A4%3C253%3ATDOAIA%3E2.0.CO%3B2-N
8
The Payoff Period and the Rate of Profit
Myron J. Gordon
The Journal of Business, Vol. 28, No. 4, Capital Budgeting. (Oct., 1955), pp. 253-260.
Stable URL:
http://links.jstor.org/sici?sici=0021-9398%28195510%2928%3A4%3C253%3ATPPATR%3E2.0.CO%3B2-A
NOTE: The reference numbering from the original has been maintained in this citation list.
http://www.jstor.org
LINKED CITATIONS
- Page 3 of 3 -
9
Hybrid Corn: An Exploration in the Economics of Technological Change
Zvi Griliches
Econometrica, Vol. 25, No. 4. (Oct., 1957), pp. 501-522.
Stable URL:
http://links.jstor.org/sici?sici=0012-9682%28195710%2925%3A4%3C501%3AHCAEIT%3E2.0.CO%3B2-A
17
A Model for the Location of a Railroad Classification Yard
Edwin Mansfield; Harold H. Wein
Management Science, Vol. 4, No. 3. (Apr., 1958), pp. 292-313.
Stable URL:
http://links.jstor.org/sici?sici=0025-1909%28195804%294%3A3%3C292%3AAMFTLO%3E2.0.CO%3B2-O
18
Measuring Recessions
Geoffrey H. Moore
Journal of the American Statistical Association, Vol. 53, No. 282. (Jun., 1958), pp. 259-316.
Stable URL:
http://links.jstor.org/sici?sici=0162-1459%28195806%2953%3A282%3C259%3AMR%3E2.0.CO%3B2-T
21
Economies of Scale, Competition, and European Integration
Tibor Scitovsky
The American Economic Review, Vol. 46, No. 1. (Mar., 1956), pp. 71-91.
Stable URL:
http://links.jstor.org/sici?sici=0002-8282%28195603%2946%3A1%3C71%3AEOSCAE%3E2.0.CO%3B2-8
NOTE: The reference numbering from the original has been maintained in this citation list.